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BRAIN IN GEAR Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills Work out what the missing words in red are. TASK EXTENSION Develop your own Mathematical letter puzzles as above. 36 I in a Y 0 R in a M 4 D to make a PC 36 Inches in a Yard 0 Runs in a Maiden 4 Digits to make a Pin Code

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Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? Nth term from picture patterns EXAMPLES 1) 2) (a) Work out the nth term for the pattern of matches (b) How many matches will the 100 th pattern have? 4 7 10 13 The diagram shows a pattern of matches building up. +3 3n+ 1 Substitute 100 into the nth term above 3 x 100+ 1 = 301 The diagram shows a pattern of squares building up. (a) How many squares will there be in the nth pattern? (b) What is the largest pattern number you can make with 187 squares? 3 5 7 +2 2n+ 1 Make the nth term equal to 187 and solve 2n + 1 = 187 - 1 2n = 186 ÷ 2 n = 93

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Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? TASK (GRADE C) Nth term from picture patterns A pattern of squares is built up from matchsticks as shown. (a) Draw the fourth diagram. (b) How many squares are there in the nth diagram? (c) How many squares are there in the 25th diagram? (d) With 200 squares, which is the biggest diagram that could be made? 1) 2) A pattern of triangles is built up from matchsticks. (a) Draw the fifth set of triangles in this pattern. (b) How many matchsticks are needed for the nth set of triangles? (c) How many matchsticks are needed to make the 60th set of triangles? (d) If there are only 100 matchsticks, which is the largest set of triangles that could be made? 3) 4) A conference centre had tables each of which could sit six people. When put together, the tables could seat people as shown. (a) How many people could be seated at four tables? (b) How many people could be seated at n tables put together in this way? (c) At a conference, 50 people wished to use the tables in this way. How many tables would they need? Regular pentagons of side length 1 cm are joined together to make a pattern as shown. Copy this pattern and write down the perimeter of each shape. (a) What is the perimeter of patterns like this made from (i) 6 pentagons (ii) n pentagons (iii) 50 pentagons? (b) What is the largest number of pentagons that can be put together like this to have a perimeter less than 1000 cm? 4n - 3 Appropriate diagram 97 50th Appropriate diagram 2n + 1 121 49th 18 4n + 2 12 20cm(3n+2)cm 152cm 332

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Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? EXTENSION (GRADE C) Nth term from picture patterns n Picking a large value of n gives an answer of zero on a calculator, so eventually the whole area will be covered.

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DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately find the nth term of a sequence from picture patterns. What grade are we working at?

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PLENARY ACTIVITY GCSE GRADE C EXAM QUESTION Consecutive patterns are put together. (a) The numbers of counters in the combined patterns form the sequence: 4, 9, 16, … How many counters will be in the next combined pattern in the sequence? (b) What type of numbers are 4, 9, 16, … ? (c) How many counters will be in the combined pattern formed by patterns 9 and 10? 25 Square numbers 10 x 10 100

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Draw your brain What have you learnt? In your brain, write or draw everything you can remember about finding the nth term of a sequence from picture patterns. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?